# Retrieval of Global Orbit Drift Corrected Land Surface Temperature from Long-term AVHRR Data

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

#### 2.1. Materials

#### 2.1.1. DTC Simulations

_{0}is the land surface temperature around sunrise, T

_{a}is the temperature amplitude, $\varpi $ is the daytime length, t

_{m}is the time for the maximum temperature, and t is the viewing time. It should be noted that there is a deviation between the cosine function and the temperature decrease after a certain moment in the evening since the change of temperature at nighttime cannot be described by a cosine function. The starting time for temperature attenuation is usually later than 17:00, so it is not included in the time range of NOAA afternoon observations. On the other hand, the temperature changes at this moment are small when compared to the changes at former moments. Even this moment is included in the NOAA overpass times, and the influence of cosine approximation is slight. Therefore, one can use a uniform cosine function to describe the temperature evolution for NOAA afternoon observations.

_{veg}, and ε

_{soil}are the effective emissivity of the pixel, vegetation, and soil, respectively; T

_{veg}and T

_{soil}are the vegetation and soil temperature, respectively; and, $f\left(\theta \right)$ is the directional fractional vegetation cover (FVC), which can be estimated by [39]

_{max}and NDVI

_{min}are the maximum and minimum NDVI, respectively, which are angle-independent and can be calculated by confidence intervals (e.g., 3% and 97%) of the NDVI image in a growing season.

_{0}, T

_{a}, $\varpi $, and t

_{m}are 297.2, 10.0, 13.0, and 17.3 for the vegetation component temperature and 290.0, 20.7, 12.0, and 17.0 for the soil component temperature, respectively (referring to Quan et al. (2014) [40]). ε

_{veg}and ε

_{soil}are prescribed as 0.98 and 0.95, respectively. Subsequently, introducing FVC and inserting the component temperatures and emissivities into Equation (2) simulates the LSTs of every pixel at any time. In practice, there is an error in LST retrieval. Therefore, a 2 K random error is added to the simulated LSTs. In addition, the observation time is sampled every 30 min. As a result, LSTs of 400 pixels with different FVCs at nine moments are generated.

#### 2.1.2. AVHRR Data

#### 2.1.3. SURFRAD LST Data

_{u}is the upward broadband hemispherical infrared flux, F

_{d}is the downward broadband hemispherical infrared flux, $\sigma $ is the Stefan–Boltzmann constant (5.670373 × 10

^{−8}), and ${\epsilon}_{3-\infty}$ is the surface broadband emissivity (BBE). The value of BBE can be calculated from narrowband emissivities while using a spectral-to-broadband linear regression equation [51,52]. Unfortunately, there are few available narrowband emissivities at SURFRAD sites before 2000. However, previous studies indicated that a 0.01 error in BBE only causes approximately a 0.1 K error in the LST [44], which is a minor contribution when compared to the contribution of the measurement uncertainties [46]. For this reason, the present study sets the same BBE values as Duan et al. [45] (see Table 1). A SURFRAD LST dataset over multiple years can be developed while combining the BBE, F

_{u}, F

_{d}, and Equation (5).

#### 2.2. Methods

#### 2.2.1. Refined GSW Algorithm

_{i}, T

_{j}are the brightness temperatures in two adjacent channels, ε is the averaged emissivity for these two channels, Δε is their emissivity difference, θ is viewing zenith angle, and A

_{0–7}are the model coefficients. It should be noticed that only the brightness temperatures of the two TIR channels are unknown inputs. The emissivities and water vapor content (WVC) have to be provided to retrieve the LST. Correspondingly, the emissivities and WVC are calculated from the NOAA AVHRR data while using the NDVI-based threshold method [39,56] and the split-window covariance–variance ratio (SWCVR) method [57], respectively. In practical application, the LST is estimated with two steps. Firstly, a preliminary LST is estimated with coefficients covering the entire LST range in a suitable WVC and averaged emissivity sub-class; then, a more accurate LST is determined while using coefficients for a suitable approximate LST sub-range [58].

#### 2.2.2. Physically-Based Orbit Drift Correction Algorithm

_{s}(14.5) is the LST at 14:30.

_{a}, $\varpi $ and t

_{m}.

_{m}, the LST at that moment is higher. Therefore, for the observation time and 14:30, the product of the difference between the time differences with t

_{m}and the difference between their LSTs should be no more than 0. That is,

_{soil}(14.5) and T

_{veg}(14.5) are the middle variables. This small range might lead to a slight influence on their accuracies, but the impact on the LST might be smaller.

_{s}(14.5) would lie between LST-15 K and LST+15 K. If the pixel is pure soil, the minimum of T

_{veg}(14.5) should be LST-30 K, and the maximum of T

_{veg}(14.5) should be LST+20 K. Based on the same scheme, T

_{soil}(14.5) should be in the range from LST-20 K to LST+30 K. Similarly, the initial values and valid ranges of the other three unknown parameters are universally set to ensure the practicality of the proposed method. The a priori knowledge of the Bayesian optimization can be obtained by solving Equation (9) with the Levenberg–Marquardt minimization method. Here, PyMC, which is a flexible and extensible Python package for Bayesian statistical models and fitting algorithms [66], and Lmfit, a high-level interface to non-linear optimization and curve fitting problems for Python [67], are selected to perform the procedure.

## 3. Results

#### 3.1. Orbit Drift Correction with Simulations

#### 3.1.1. Performance

_{m}when the variation in the LST is more dramatic. The proposed ODC algorithm uses the relationship between the LST at t

_{m}and the LST at the viewing time as well as at 14:30. Therefore, a more dramatic variation might lead to a bad ability to find a stable solution. However, owing to ODC, the Bias becomes closer to 0 from 1.3 to 0.3 K, which suggests that the estimated LSTs at 14:30 have a more similar trend to the actual LSTs at 14:30 than the original LSTs at 13:30. For this reason, the correction method is still useful, even though it leads to a slight RMSE increase. As far as 14:00 and 15:00 are concerned, since both times are close to 14:30, there is almost not change in the RMSEs before and after ODC. However, the absolute Biases reduce to 0.7 K, both for 14:00 and 15:00, again illustrating the validity of the proposed method. For other moments, the correction effects are more significant. The RMSEs decreased to 0.7 K, 1.2 K, 2.4 K, and 3.9 K, and the absolute Biases reduced to 1.3 K, 2.0 K, 3.7 K, and 5.7 K for 15:30, 16:00, 16:30, and 17:00, respectively. However, from the perspective of absolute accuracy, the RMSEs are 2.2 K (14:00 and 15:00), 2.3 K (15:30), 2.5 K (16:00), and 2.6 K (16:30 and 17:00). Obviously, the further the viewing time is from 14:30, the larger the correction error is. This result is expected, since a large time difference would create more difficulty in normalization. Overall, the majority of differences between the actual LST and the estimated LST at 14:30 are within the range of (−3, 3) K, and the proportions of 13:30, 14:00, 15:00, 15:30, 16:00, 16:00, and 17:00 are 72.9%, 81.7%, 82.2%, 80.2%, 78.7%, 73.7%, and 74.2%, respectively. Almost of all the differences are within the range of (−5, 5) K, and the minimum proportion is 94.2 % at 17:00. While considering that the prescribed LST error is 2 K, these correction results are encouraging.

#### 3.1.2. Sensitivity Analysis

#### 3.2. Validation

#### 3.2.1. LST Retrieval

^{2}[49]. Therefore, large RMSEs (>2 K) are expected. There are different land covers, homogeneity, and orography within such a big pixel, which could exert considerable influence on LST validation [43,46]. On the other hand, only observations during daytime are used since the temporal resolution of LTDR data is once a day, meaning that there is high thermal heterogeneity [43,45,46]. Nevertheless, the retrieval accuracy is also encouraging. Martin et al. [46] evaluated five LST products from various sensors (AATSR, GOES, MODIS, and SEVIRI) by using in-situ datasets over multiple stations and years and concluded that the average accuracies over the entire time span are within ±2.0 K during nighttime and within ±4.0 K during daytime. Duan et al. [45] also reported that large RMSE values (>2 K) of the collection 6 MODIS LST were obtained during daytime based on the in-situ measurements. Therefore, the results from the NOAA data in this study are competitive.

#### 3.2.2. Orbit Drift Correction

#### 3.3. Application

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Equatorial Crossing Time (ECT) for National Oceanic and Atmospheric Administration (NOAA) afternoon Satellites (Adapted from https://www.star.nesdis.noaa.gov/smcd/emb/vci/VH/vh_avhrr_ect.php).

**Figure 2.**Schematic diagram of the diurnal temperature cycle (DTC) model [Adapted from Duan et al. [38].

**Figure 4.**The result of the orbit drift correction for (

**a**) the entire interval and (

**b**–

**h**) different moments. The subscript ‘Ori’ represents the simulated land surface temperatures (LSTs) at the original viewing time, and ‘ODC’ represents the corrected LSTs at 14:30, estimated from the corresponding time. The solid line represents 1:1, the two dashed lines are 1:1 ± 3 K, and the two dashdot lines are 1:1 ± 5 K.

**Figure 5.**Sensitivity of the physically-based orbit drift correction algorithm for LST retrieval error.

**Figure 6.**Sensitivity of the physically-based orbit drift correction algorithm to fractional vegetation cover (FVC) retrieval error.

**Figure 7.**Scatterplots of the retrieved NOAA-14 LST versus the in-situ SURFRAD LST for all matched days over (

**a**) Bondville (BND), (

**b**) Table Mountain (TBL), (

**c**) Desert Rock (DRA), (

**d**) Fort Peck (FPK), (

**e**) Goodwin Creek (GWN), and (

**f**) Pennsylvania State University (PSU).

**Figure 8.**Scatterplots of the retrieved NOAA-14 LST at different VZA sub-groups versus the in-situ SURFRAD LST over (

**a**) BND, (

**b**) TBL, (

**c**) DRA, (

**d**) FPK, (

**e**) GWN, and (

**f**) PSU.

**Figure 9.**Seasonal root-mean-square error (RMSE) and Bias of the retrieved NOAA-14 LST over (

**a**) BND, (

**b**) TBL, (

**c**) DRA, (

**d**) FPK, (

**e**) GWN, and (

**f**) PSU.

**Figure 10.**Scatterplots of the retrieved NOAA-14 LST versus the in-situ SURFRAD LST for days in which the sky is cloudless at 14:30 over (

**a**) BND, (

**b**) TBL, (

**c**) DRA, (

**d**) FPK, (

**e**) GWN, and (

**f**) PSU.

**Figure 11.**The results of orbit drift correction over (

**a**) BND, (

**b**) TBL, (

**c**) DRA, (

**d**) FPK, (

**e**) GWN, and (

**f**) PSU. The abbreviation ‘Ori’ represents the retrieved LSTs at the original viewing time, and ‘ODC’ represents the corrected LSTs at 14:30, as estimated from the corresponding time.

**Figure 12.**Scatterplots of the ΔLST (retrieved NOAA LST–in-situ SURFRAD LST) at the original viewing time versus ΔLST (corrected NOAA LST–in-situ SURFRAD LST) at 14:30 over (

**a**) BND, (

**b**) TBL, (

**c**) DRA, (

**d**) FPK, (

**e**) GWN, and (

**f**) PSU.

**Figure 13.**The LSTs over a grassland pixel (114.3 °N, 41.1 °E) from 1981 to 2017. (

**a**) the original LST at overpass time using the improved GSW algorithm; (

**b**) the corrected LST at 14:30 while using the proposed ODC algorithm; and, (

**c**) the ΔLST (corrected LST at 14:30–original LST at overpass time) and the corresponding overpass time. The three black rectangles, from left to right, are the LSTs from 1992 to 1994, LSTs from 1999 to 2000, and LSTs from 2005 to 2006, respectively.

**Figure 14.**The influence of FVC standard deviation (STD) on the physically-based orbit drift correction algorithm.

Station Name | Lon (°W) | Lat (°N) | Elevation (m) | Installed Time | Land Cover Type | Broadband Emissivity |
---|---|---|---|---|---|---|

BND | 88.373 | 40.051 | 230 | April 1994 | Cropland | 0.968 |

TBL | 105.238 | 40.126 | 1689 | July 1995 | Bare soil | 0.972 |

DRA | 116.020 | 36.623 | 1007 | March 1998 | Bare soil | 0.967 |

FPK | 105.102 | 48.308 | 634 | November 1994 | Grassland | 0.973 |

GWN | 89.873 | 34.255 | 98 | December 1994 | Grassland | 0.971 |

PSU | 77.931 | 40.720 | 376 | June 1998 | Cropland | 0.970 |

Parameter | Initial Value | Minimum | Maximum |
---|---|---|---|

${T}_{veg}\left(14.5\right)$ (K) | LST | LST-30 | LST+20 |

${T}_{soil}\left(14.5\right)$ (K) | LST | LST-20 | LST+30 |

${T}_{a}$ (K) | 20 | 5 | 30 |

$\varpi $ (h) | 13 | 10 | 16 |

${t}_{m}$ (h) | 13 | 12 | 15 |

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Liu, X.; Tang, B.-H.; Yan, G.; Li, Z.-L.; Liang, S.
Retrieval of Global Orbit Drift Corrected Land Surface Temperature from Long-term AVHRR Data. *Remote Sens.* **2019**, *11*, 2843.
https://doi.org/10.3390/rs11232843

**AMA Style**

Liu X, Tang B-H, Yan G, Li Z-L, Liang S.
Retrieval of Global Orbit Drift Corrected Land Surface Temperature from Long-term AVHRR Data. *Remote Sensing*. 2019; 11(23):2843.
https://doi.org/10.3390/rs11232843

**Chicago/Turabian Style**

Liu, Xiangyang, Bo-Hui Tang, Guangjian Yan, Zhao-Liang Li, and Shunlin Liang.
2019. "Retrieval of Global Orbit Drift Corrected Land Surface Temperature from Long-term AVHRR Data" *Remote Sensing* 11, no. 23: 2843.
https://doi.org/10.3390/rs11232843